Jaeho Haan
Korea Advanced Institute of Science and Technology · 数学
研究室紹介
Professor Jaeho Haan's research focuses on automorphic forms, L-functions, and the Langlands program, with a particular emphasis on the local and global Gan-Gross-Prasad conjectures, theta correspondence, and Bessel/Fourier-Jacobi periods for classical and metaplectic groups. His work explores the interplay between representation theory, L-values, and functoriality, especially in non-tempered and non-generic settings, often using theta correspondence and regularized periods to establish rigidity and stability results. He investigates the local and global structures of automorphic representations, particularly for unitary and orthogonal groups, and contributes to the refinement of duality conjectures in the context of the Langlands program.
Research Overview
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Selected Papers
15Abstract Let F be a non-archimedean local field of characteristic not equal to 2. In this article, we prove the local converse theorem for quasi-split $\mathrm {O}_{2n}(F)$ and $\mathrm {SO}_{2n}(F)$ , via the description of the local theta correspondence between $\mathrm {O}_{2n}(F)$ and $\mathrm {Sp}_{2n}(F)$ . More precisely, as a main step, we explicitly describe the precise behavior of the $\gamma $ -factors under the correspondence. Furthermore, we apply our results to prove the weak rigid
In \cite{Ha}, Neal Harris has given a refined Gross-Prasad conjecture for unitary group as an analogue of Ichino and Ikeda's paper \cite{Ich} concerning special orthogonal groups. In his paper, he stated a conjecture under the assumption that the pair of given representations should be tempered. In this paper, we consider a specific pair involving a non-tempered one. In this case, an analogous formula still exists but the central critical $L$-value is slightly different with the one in the conje
In this paper, we study the restriction problem of representations for a non-tempered Arthur packet of $U(3)$. For a pair of tempered $L$-parameters of $(U(n),U(n-1))$, it is known that there is a unique pair of representations in their associateed Vogan $L$-packets which produces the unique Bessel model of these $L$-parameters. We showed that this is ture for some pair of $L$-parameters involving a non-tempered one. On the other hand, we give the precise local theta correspondence for $(U(1),U(
In this paper, we prove one direction of the Gan--Gross--Prasad conjecture on metaplectic-symplectic groups for tempered cases. Furthermore, we also prove one direction of the non-tempered GGP conjecture for residual representations with relevant $A$-parameters. As an application, we discuss the non-vanishing of the central value of quadratic twists of automorphic $L$-functions of $GL_{2n}$.
In this paper, we establish a relationship between special periods and special L-values of automorphic representations of classical groups, and prove the non-tempered global Gan--Gross--Prasad conjecture in several cases. Our approach consists of two main steps. First, inspired by Rallis' tower property, we study the interaction between special periods and the tower property for the genericity of global theta lifts. Second, we investigate the relationship between the analytic properties of L-fun
Abstract In this paper, we establish the local converse theorem and the stability of local gamma factors for $$\widetilde{\textrm{Sp}}_{2n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mtext>Sp</mml:mtext> <mml:mo>~</mml:mo> </mml:mover> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:math> via the precise local theta correspondence between $$\widetilde{\textrm{Sp}}_{2n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/M
In this paper, we introduce regularized trilinear periods on certain non-reductive groups. It has two direct applications. Firstly, it enables us to define the regularized Bessel periods and the regularized Fourier-Jacobi periods for all classical and metaplectic groups. Secondly, by using the properties of the regularized Fourier-Jacobi periods, we can prove one direction of the full Gan-Gross-Prasad conjecture on skew-hermitian unitary groups.
The local Gan-Gross-Prasad conjecture of unitary groups, which is now settled by the works of Beuzart-Plessis, Gan and Ichino, says that for a pair of generic L-parameters of (U(n+1), U(n)), there is a unique pair of representations in their associated Vogan L-packets which produces the Bessel model. In this survey article, we report that the conjecture does not hold for a non-generic case.
In this paper, we establish the local converse theorem and the stability of local gamma factors for $\Mp_{2n}$ via the precise local theta correspondence between $\Mp_{2n}$ and $\SO_{2n+1}$ over local fields of characteristic not equal to 2. We also prove the rigidity theorem for irreducible generic cuspidal automorphic representations of $\Mp_{2n}$ over number fields.
In this paper, we investigate the local Gan-Gross-Prasad conjecture for some pair of representations of $U(3)\times U(2)$ involving a non-generic representation. For a pair of generic $L$-parameters of $(U(n),U(n-1))$, it is known that there is a unique pair of representations in their associateed Vogan $L$-packets which produces the unique Bessel model of these $L$-parameters. We showed that this is not ture for some pair of $L$-parameters involving a non-generic one. On the other hand, we give